Theory of Composite Fermions

0240458

Jain

This award supports fundamental theoretical research and education involving the fractional quantum Hall effect. The PI will continue his work on composite fermions, electrons bound to an even number of quantized vortices. Most of the qualitative phenomenology of the fractional quantum Hall effect can be understood by neglecting the residual interaction between composite fermions. In recent years, improved experiments have revealed subtle features that go beyond this model. The main goal of this research is to study the effects of interaction between composite fermions to explain existing experimental anomalies and make predictions for future experiments. The PI will also use recently developed techniques to further refine the quantitative accuracy of the theory, which should shed light on several interesting questions, for example, the competition between the Wigner solid and the fractional Hall liquid, and the physics of edge states. Broader impacts of this work include graduate level training of the next generation of condensed matter theorists in the areas of quantum mechanics, many body physics, nanophysics. Students will also learn a wide range of modern numerical techniques, including the Monte Carlo method and gain proficiency in the use of parallel computers. Fundamental research on two-dimensional electron systems has helped drive spectacular improvements in materials quality, especially in GaAs semiconductors.

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A system of many electrons may act in surprising ways that cannot be extrapolated from the knowledge of the behavior of a single particle. Its understanding requires fundamentally new concepts. This award supports fundamental theoretical research and education on one such system, electrons confined to two dimensions at the interface between two semiconductors, cooled to low temperatures and exposed to a strong magnetic field. Electrons in this system exhibit integral and fractional quantum Hall effects, and at the same time provide realizations of subtle quantum mechanical states including Wigner crystals, skyrmions, stripes, and Tomonaga-Luttinger liquids. While progress has been made toward understanding various aspects of the fractional Hall effect, this research focuses on new regimes where many new quantum mechanical states are likely to be discovered and will focus on advancing the theory of composite fermions, electrons bound to an even number of quantized vortices, which currently captures the qualitative features of the fractional quantum Hall regime. Anomalies observed in recent experiments provide motivation for this work.

This award contributes to the education of the next generation of condensed matter theorists in the areas of quantum mechanics, many body physics, and the physics of nanoscale systems. Students will also learn appropriate related numerical techniques, including the Monte Carlo method, and gain proficiency in the use of parallel computers. Fundamental research on two dimensional electrons systems has helped drive spectacular improvements in materials quality, especially in GaAs semiconductors.

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